Semivariance : definition of Semivariance and synonyms of Semivariance (English)

It has been suggested that this article or section be merged into Variogram. (Discuss) Proposed since January 2010.

In spatial statistics, the empirical semivariance is described by

$\hat\gamma(h)=\frac{1}{2}\cdot\frac{1}{n(h)}\sum_{i=1}^{n(h)}(z(x_i+h)-z(x_i))^2$

where z is a datum at a particular location, h is the distance between ordered data, and n(h) is the number of paired data at a distance of h. The semivariance is half the variance of the increments $z(x_i+h)-z(x_i)$ , but the whole variance of z-values at given separation distance h (Bachmaier and Backes, 2008).

A plot of semivariances versus distances between ordered data in a graph is known as a semivariogram rather than a variogram. Many authors call $2\hat\gamma(h)$ a variogram, others use the terms variogram and semivariogram synonymously. However, Bachmaier and Backes (2008), who discussed this confusion, have shown that $\hat\gamma(h)$ should be called a variogram, terms like semivariogram or semivariance should be avoided.

References

Bachmaier, M and Backes, M, 2008, "Variogram or Semivariogram — Explaining the Variances in a Variogram". Article doi:10.1007/s11119-008-9056-2, Precision Agriculture, Springer-Verlag, Berlin, Heidelberg, New York.
Clark, I, 1979, Practical Geostatistics, Applied Science Publishers
David, M, 1978, Geostatistical Ore Reserve Estimation, Elsevier Publishing
Hald, A, 1952, Statistical Theory with Engineering Applications, John Wiley & Sons, New York
Journel, A G and Huijbregts, Ch J, 1978 Mining Geostatistics, Academic Press

External links

Shine, J.A., Wakefield, G.I.: A comparison of supervised imagery classification using analyst-chosen and geostatistically-chosen training sets, 1999, http://www.geovista.psu.edu/sites/geocomp99/Gc99/044/gc_044.htm

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